{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 0
   },
   "source": [
    "# 多层感知机的从零开始实现\n",
    ":label:`sec_mlp_scratch`\n",
    "\n",
    "我们已经在数学上描述了多层感知机（MLP），现在让我们尝试自己实现一个多层感知机。为了与我们之前使用softmax回归（ :numref:`sec_softmax_scratch` ）获得的结果进行比较，我们将继续使用Fashion-MNIST图像分类数据集（ :numref:`sec_fashion_mnist`）。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "origin_pos": 2,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\WeiWu-GU\\anaconda3\\envs\\pte\\lib\\site-packages\\ipykernel\\pylab\\backend_inline.py:164: DeprecationWarning: `configure_inline_support` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.configure_inline_support()`\n",
      "  configure_inline_support(ip, backend)\n"
     ]
    }
   ],
   "source": [
    "import paddle\n",
    "from paddle import nn\n",
    "from d2l import torch as d2l\n",
    "import pd2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "origin_pos": 4,
    "scrolled": false,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\WeiWu-GU\\anaconda3\\envs\\pte\\lib\\site-packages\\ipykernel\\ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.\n",
      "  and should_run_async(code)\n"
     ]
    }
   ],
   "source": [
    "batch_size = 256\n",
    "train_iter, test_iter = pd2l.load_data_fashion_mnist(batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 5
   },
   "source": [
    "## 初始化模型参数\n",
    "\n",
    "回想一下，Fashion-MNIST中的每个图像由$28 \\times 28 = 784$个灰度像素值组成。所有图像共分为10个类别。忽略像素之间的空间结构，我们可以将每个图像视为具有784个输入特征和10个类的简单分类数据集。首先，我们将[**实现一个具有单隐藏层的多层感知机，它包含256个隐藏单元**]。注意，我们可以将这两个量都视为超参数。通常，我们选择2的若干次幂作为层的宽度。因为内存在硬件中的分配和寻址方式，这么做往往可以在计算上更高效。\n",
    "\n",
    "我们用几个张量来表示我们的参数。注意，对于每一层我们都要记录一个权重矩阵和一个偏置向量。跟以前一样，我们要为这些参数的损失的梯度分配内存。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "origin_pos": 7,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "num_inputs, num_outputs, num_hiddens = 784, 10, 256\n",
    "\n",
    "W1 = paddle.randn([num_inputs, num_hiddens]) * 0.01\n",
    "W1.stop_gradient = False\n",
    "b1 = paddle.zeros([num_hiddens])\n",
    "b1.stop_gradient = False\n",
    "W2 = paddle.randn([num_hiddens, num_outputs]) * 0.01\n",
    "W2.stop_gradient = False\n",
    "b2 = paddle.zeros([num_outputs])\n",
    "b2.stop_gradient = False\n",
    "\n",
    "params = [W1, b1, W2, b2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 9
   },
   "source": [
    "## 激活函数\n",
    "\n",
    "为了确保我们知道一切是如何工作的，我们将使用最大值函数自己[**实现ReLU激活函数**]，而不是直接调用内置的`relu`函数。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "origin_pos": 11,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def relu(X):\n",
    "    a = paddle.zeros_like(X)\n",
    "    return paddle.max(X, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 13
   },
   "source": [
    "## 模型\n",
    "\n",
    "因为我们忽略了空间结构，所以我们使用`reshape`将每个二维图像转换为一个长度为`num_inputs`的向量。我们只需几行代码就可以(**实现我们的模型**)。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "origin_pos": 15,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def net(X):\n",
    "    X = X.reshape((-1, num_inputs))\n",
    "    H = relu(X@W1 + b1)  # 这里“@”代表矩阵乘法\n",
    "    return (H@W2 + b2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 17
   },
   "source": [
    "## 损失函数\n",
    "\n",
    "为了确保数值稳定性，同时由于我们已经从零实现过softmax函数（ :numref:`sec_softmax_scratch` ），因此在这里我们直接使用高级API中的内置函数来计算softmax和交叉熵损失。回想一下我们之前在 :numref:`subsec_softmax-implementation-revisited` 中对这些复杂问题的讨论。我们鼓励感兴趣的读者查看损失函数的源代码，以加深对实现细节的了解。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "origin_pos": 19,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "loss = nn.CrossEntropyLoss()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 21
   },
   "source": [
    "## 训练\n",
    "\n",
    "幸运的是，[**多层感知机的训练过程与softmax回归的训练过程完全相同**]。可以直接调用`d2l`包的`train_ch3`函数（参见 :numref:`sec_softmax_scratch` ），将迭代周期数设置为10，并将学习率设置为0.1.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "origin_pos": 23,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "(InvalidArgument) Input(Y) has error dim.Y'dims[0] must be equal to 1But received Y'dims[0] is 256\n  [Hint: Expected y_dims[y_ndim - 2] == N, but received y_dims[y_ndim - 2]:256 != N:1.] (at C:\\home\\workspace\\Paddle_release\\paddle/fluid/operators/matmul_v2_op.h:164)\n  [operator < matmul_v2 > error]",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-18-00a2951881b8>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mnum_epochs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mupdater\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpaddle\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0moptimizer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mSGD\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlearning_rate\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mlr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparameters\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mpd2l\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtrain_ch3\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrain_iter\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtest_iter\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mloss\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnum_epochs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mupdater\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mD:\\workspace\\d2ltopaddle\\chapter_multilayer-perceptrons\\pd2l.py\u001b[0m in \u001b[0;36mtrain_ch3\u001b[1;34m(net, train_iter, test_iter, loss, num_epochs, updater)\u001b[0m\n\u001b[0;32m    324\u001b[0m                         legend=['train loss', 'train acc', 'test acc'])\n\u001b[0;32m    325\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mepoch\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnum_epochs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 326\u001b[1;33m         \u001b[0mtrain_metrics\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtrain_epoch_ch3\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrain_iter\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mloss\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mupdater\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    327\u001b[0m         \u001b[0mtest_acc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mevaluate_accuracy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtest_iter\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    328\u001b[0m         \u001b[0manimator\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0madd\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mepoch\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrain_metrics\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mtest_acc\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\workspace\\d2ltopaddle\\chapter_multilayer-perceptrons\\pd2l.py\u001b[0m in \u001b[0;36mtrain_epoch_ch3\u001b[1;34m(net, train_iter, loss, updater)\u001b[0m\n\u001b[0;32m    259\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mtrain_iter\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    260\u001b[0m         \u001b[1;31m# Compute gradients and update parameters\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 261\u001b[1;33m         \u001b[0my_hat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnet\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    262\u001b[0m         \u001b[0ml\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mloss\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my_hat\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    263\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mupdater\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpaddle\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0moptimizer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mOptimizer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-16-872339a7efc2>\u001b[0m in \u001b[0;36mnet\u001b[1;34m(X)\u001b[0m\n\u001b[0;32m      2\u001b[0m     \u001b[0mX\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnum_inputs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m     \u001b[0mH\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrelu\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m@\u001b[0m\u001b[0mW1\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mb1\u001b[0m\u001b[1;33m)\u001b[0m  \u001b[1;31m# 这里“@”代表矩阵乘法\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mH\u001b[0m\u001b[1;33m@\u001b[0m\u001b[0mW2\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mb2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\anaconda3\\envs\\pte\\lib\\site-packages\\paddle\\fluid\\dygraph\\math_op_patch.py\u001b[0m in \u001b[0;36m__impl__\u001b[1;34m(self, other_var)\u001b[0m\n\u001b[0;32m    248\u001b[0m             \u001b[0maxis\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    249\u001b[0m             \u001b[0mmath_op\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcore\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mops\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mop_type\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 250\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mmath_op\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mother_var\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'axis'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    251\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    252\u001b[0m         \u001b[0mcomment\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mOpProtoHolder\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_op_proto\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mop_type\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomment\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: (InvalidArgument) Input(Y) has error dim.Y'dims[0] must be equal to 1But received Y'dims[0] is 256\n  [Hint: Expected y_dims[y_ndim - 2] == N, but received y_dims[y_ndim - 2]:256 != N:1.] (at C:\\home\\workspace\\Paddle_release\\paddle/fluid/operators/matmul_v2_op.h:164)\n  [operator < matmul_v2 > error]"
     ]
    }
   ],
   "source": [
    "num_epochs, lr = 10, 0.1\n",
    "updater = paddle.optimizer.SGD(learning_rate=lr, parameters=params)\n",
    "pd2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 25
   },
   "source": [
    "为了对学习到的模型进行评估，我们将[**在一些测试数据上应用这个模型**]。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "origin_pos": 26,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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     },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "d2l.predict_ch3(net, test_iter)"
   ]
  },
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   "metadata": {
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   },
   "source": [
    "## 小结\n",
    "\n",
    "* 我们看到即使手动实现一个简单的多层感知机也是很容易的。\n",
    "* 然而，如果有大量的层，从零开始实现多层感知机会变得很麻烦（例如，要命名和记录模型的参数）。\n",
    "\n",
    "## 练习\n",
    "\n",
    "1. 在所有其他参数保持不变的情况下，更改超参数`num_hiddens`的值，并查看此超参数的变化对结果有何影响。确定此超参数的最佳值。\n",
    "1. 尝试添加更多的隐藏层，并查看它对结果有何影响。\n",
    "1. 改变学习速率会如何影响结果？保持模型结构和其他超参数(包括迭代周期数)不变，学习率设置为多少会带来最好的结果？\n",
    "1. 通过对所有超参数(学习率、迭代周期数、隐藏层数、每层的隐藏单元数)进行联合优化，可以得到的最佳结果是什么？\n",
    "1. 描述为什么涉及多个超参数更具挑战性。\n",
    "1. 如果要构建多个超参数的搜索方法，你能想到的最聪明的策略是什么？\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 29,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "[Discussions](https://discuss.d2l.ai/t/1804)\n"
   ]
  }
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